ON THE MINIMAXNESS AND ARTINIANNESS DIMENSIONS | ||
| Journal of Algebraic Systems | ||
| دوره 11، شماره 2، فروردین 2024، صفحه 137-145 اصل مقاله (139.7 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11553.1584 | ||
| نویسندگان | ||
| Jafar Azami* 1؛ Mohammad Reza Doustimehr2 | ||
| 1Department of Mathematics, University of Mohaghegh Ardabili, Ardabil, Iran. | ||
| 2Department of Mathematics, University of Tabriz, Tabriz, Iran; and School of Mathematics, Institute for research in fundamental sciences (IPM), P.O. Box 19395-5746, Tehran, Iran. | ||
| چکیده | ||
| Let R be a commutative Noetherian ring, I, J be ideals of R such that J ⊆ I, and M be a finitely generated R-module. In this paper, we prove that the invariants AJI (M) := inf{i ∈ N0 | JtHi I (M) is not Artinian for all t ∈ N0} and inf{i ∈ N0 | JtHi I (M) is not minimax for all t ∈ N0} are equal. In particular, we show that the invariants AII (M) and inf{i ∈ N0 | Hi I (M) is not minimax} are equal. We also establish the local-global principle, AJI (M) = inf{AJRp IRp (Mp)|p ∈ Spec (R)}, in some cases. | ||
| کلیدواژهها | ||
| Local cohomology؛ Artinian module؛ minimax module؛ finiteness dimension | ||
| مراجع | ||
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